ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 11 Sep 2020 12:28:25 -0500Changing Parent on multivariable polynomial ringhttp://ask.sagemath.org/question/53403/changing-parent-on-multivariable-polynomial-ring/ This question is similar to
https://ask.sagemath.org/question/8035/changing-parent-rings-of-polynomials/
R.<x,y,z,w> = QQ[]
f=x*y*z*w
f1=derivative(f,x)
f2=derivative(f,y)
f3=derivative(f,z)
f4=derivative(f,w)
J = R.ideal([f1, f2, f3,f4])
Now f is in its Jacobian by Euler identity so we can lift f as follows.
f in J
returns true.
f.lift(J)
returns the lift of f. Now consider h=f^(2)/ (x*y*z). Although this seems like a rational function, this is actually a polynomial.
h in J
returns true. However, I get an error when doing
h.lift(J)
The reason for this is Sage reads h as living not in the multivariable ring, but the fraction field of it because I divided by x*y*z. Apparently, there is no lift function for polynomials living in the fraction field. However, it is still an honest polynomial as it divides cleanly with no remainder. To be more clear,
f.parent()
returns Multivariate Polynomial Ring in x, y, z, w over Rational Field.
h.parent()
returns Fraction Field of Multivariate Polynomial Ring in x, y, z, w over Rational Field. Is there a way to make h belong to the multivariate ring instead of its fraction field so I can apply the lift function?whatupmattFri, 11 Sep 2020 12:28:25 -0500http://ask.sagemath.org/question/53403/Converting polynomials between ringshttp://ask.sagemath.org/question/24207/converting-polynomials-between-rings/ I have two polynomials, each one explicitly created as members of different multivariate polynomial rings. So for example I might have
R1.<a,b,c,t> = PolynomialRing(QQ)
L = (a*t^2+b*t+c).subs(a=2,b=3,c=4)
R2.<A,B,C,D,t> = PolynomialRing(QQ)
p = (A*t+B)^2+(C*t+D)^2
Now I want to compare the coefficients of the two polynomials, which means converting L to be a polynomial in the ring R2.
However, I'm not sure (or more to the point, can't remember) how to do this. Is there some simple, canonical way to do this? Thanks!AlasdairFri, 19 Sep 2014 07:44:21 -0500http://ask.sagemath.org/question/24207/